It has previously been shown that subnets differ from global networks from which they are sampled for all but a very limited number of theoretical network models. These differences are of qualitative as well as quantitative nature, and the properties of subnets may be very different from the corresponding properties in the true, unobserved network. Here we propose a novel approach which allows us to infer aspects of the true network from incomplete network data in a multi-model inference framework. We develop the basic theoretical framework, including procedures for assessing confidence intervals of our estimates and evaluate the performance of this approach in simulation studies and against subnets drawn from the presently available PIN network data in Saccaromyces cerevisiae. We then illustrate the potential power of this new approach by estimating the number of interactions that will be detectable with present experimental approaches in sfour eukaryotic species, inlcuding humans. Encouragingly, where independent datasets are available we obtain consistent estimates from different partial protein interaction networks. We conclude with a discussion of the scope of this approaches and areas for further research.